Harang, 33, went 14-7 with a career-best 3.64 ERA in 28 starts with the Padres this past season, his first with the club. A 10-year MLB veteran, Harang has also spent time with the Athletics and Reds.
The 32-year-old Hawpe hit .231 in 62 games with the Padres in 2011 before undergoing season-ending Tommy John surgery in June. He has also spent time with the Rockies and Rays during his eight-year career.
Qualls led San Diego with 77 relief appearances this past season, his most since making 77 appearances as a member of the Diamondbacks in 2008. The 33- year-old went 6-8 with a 3.51 ERA and 43 strikeouts against 20 walks in 2011. He has posted a 3.78 ERA over eight MLB season with the Astros, Diamondbacks, Rays and Padres.